Adaptive estimation of heavy right tails: resampling-based methods in action
In this paper, we discuss an algorithm for the adaptive estimation of a positive extreme value index, γ, the primary parameter in Statistics of Extremes. Apart from the classical extreme value index estimators, we suggest the consideration of associated second-order corrected-bias estimators, and propose the use of resampling-based computer-intensive methods for an asymptotically consistent choice of the thresholds to use in the adaptive estimation of γ. The algorithm is described for a classical γ-estimator and associated corrected-bias estimator, but it can work similarly for the estimation of other parameters of extreme events, like a high quantile, the probability of exceedance or the return period of a high level.
KeywordsStatistics of extremes Semi-parametric estimation Resampling-based methodology
AMS 2000 Subject ClassificationsPrimary—62G32 62E20; Secondary—65C05
Unable to display preview. Download preview PDF.
- Fraga Alves, M.I., Gomes M.I., de Haan, L.: A new class of semi-parametric estimators of the second order parameter. Port. Math. 60(2), 194–213 (2003)Google Scholar
- Geluk, J., de Haan, L.: Regular Variation, Extensions and Tauberian Theorems. CWI Tract 40, Center for Mathematics and Computer Science, Amsterdam, Netherlands (1987)Google Scholar
- Gomes, M.I., de Haan, L., Henriques-Rodrigues, L.: Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses. J. R. Stat. Soc. B70(1), 31–52 (2008c)Google Scholar